Hee! This is just a personal observation, but in any game I've ever played, if the other guy has Mech Infantry, it's too late to declare war.
Also, tanks are almost worthless as city defenders. They don't get any defensive bonues.
Oh no...it can be done. Even if you're backward.
I still remember a game where darius ran away with the game and was close to space. It was an islands game, an every island had about 6-8 cities. Darius had 8. I had two islands. Mech infantry be damned, I took every coastal city he had with marines. I forget the logistics of how I did it then (it was a couple months ago when I'd only started winning monarch ---> emperor), but if I were to do it now I'd use a very large naval stack and fighters/marines, or if somehow nukes aren't banned and he didn't have uranium those. Marines launch the amphibious assault on damaged garrisons (unlike blimps, a decent # of fighters can cut defenders to 1/2 strength, and there's nothing in the game that will defend well vs marines if defending at 1/2 strength), then the city is stocked with CG mechs of your own. I think back then I just beat him with pure marine spam though. Promo advantage = not so easy to attack CG II-III marines even if that's suboptimal.
I recommend keeping it completely amphibious at this point though, unless you have a reliable way to both land and deal with the AI stack without it using railroads to slam a ton of collateral into you. On an islands map there's no choice but amphibious although if they have a border with someone else you could conceivably invade from there and bait them by taking a city and keeping your real stack away from it until it's taken back.
Still, the coastal strike works very well. You can just keep taking cities. As the AI takes them back (if it manages through tough CG units) it will lose units both through direct losses and leaving garrisons behind as it rushes to re-capture its cities. Eventually, its stack runs out and then you start actually keeping cities. Given the speed of modern navies, this process can occur pretty quickly. The reason I prefer it is that you control when/where/how you engage the AI stack, which is very difficult against an intercontinental opponent with rails and a large stack + collateral.
Of course, this necessitates a decent navy, but then again fighters help there too, or alternatively you can hunt down where they're keeping the bulk of the navy and take that down turn 1 (recommended).
Mech infantry aren't all that scary. And on regular land wars air superiority or mobile arty + modern armor with CR can cut them down pretty easily too (or even just modern armor/mechs with spies to drop defenses in many cases, as by then CR III MA isn't impossible). Usually fighters on intercept can be useful though.
) but I couldn't since it wasn't the founding city. I can't t remember even having a choice when the religion was founded. 
